Rewrite the function by completing the square. $f(x)=x^{2}+8x+4$ $f(x)=(x+$
Explanation: We want to complete $x^2{+8}x$ into a perfect square. To do that, we should add $\left(\dfrac{{+8}}{2}\right)^2={16}$ to it: $x^2{+8}x+{16}=(x+4)^2$ In order to keep the expression equivalent, we add and subtract ${16}$, not forgetting the expression's constant term, $4$ : $\begin{aligned} f(x)&=x^2+8x+4 \\\\ &=x^2+8x+{16}+4-{16} \\\\ &=(x+4)^2+4-16 \\\\ &=(x+4)^2-12 \end{aligned}$ In conclusion, after completing the square, the function is written as $f(x)=(x + 4)^2 - 12$